# Cubic Function of a Cylinder

• Oct 4th 2009, 09:21 AM
fizz
Cubic Function of a Cylinder
A rectangular piece of sheet metal with perimeter 50cm is rolled into a cylinder with open ends.

a) Express the volume of the cylinder as a function of x. Then give the domain of the function.
b) Find the approximate value of x that maximizes the volume. Then give the approximate maximum volume.
• Oct 4th 2009, 09:54 AM
skeeter
Quote:

Originally Posted by fizz
A rectangular piece of sheet metal with perimeter 50cm is rolled into a cylinder with open ends.

a) Express the volume of the cylinder as a function of x. Then give the domain of the function.
b) Find the approximate value of x that maximizes the volume. Then give the approximate maximum volume.

what is x supposed to represent?
• Oct 4th 2009, 10:07 AM
fizz
The circumference of the cylinder. Sorry, I forgot to include that.
• Oct 4th 2009, 10:24 AM
skeeter
side of the rectangular sheet that forms the circumference, $\displaystyle C = x$

adjacent side that forms the height of the cylinder, $\displaystyle h = 25-x$

$\displaystyle x = 2\pi r$

$\displaystyle r = \frac{x}{2\pi}$

substitute in the expressions for $\displaystyle r$ and $\displaystyle h$ in terms of $\displaystyle x$ into the cylinder volume formula, then maximize.